The provided code is a computational model designed to simulate key aspects of neural network dynamics within the cortex, specifically focusing on excitatory and inhibitory neuron populations. Here’s a breakdown of the biological basis for the components modeled in the code: ### Neuron Types 1. **Excitatory Neurons:** - The model includes a large population of excitatory neurons, which reflect the majority of neurons in cortical networks. - These neurons are based on the Morris-Lecar (ML) model, a type of conductance-based model that captures the ionic currents underlying action potential generation. - Excitatory neurons have parameters set for sodium (Na⁺), potassium (K⁺), and leak currents, which are crucial for neuronal excitability and firing. 2. **Inhibitory Neurons:** - A smaller population of inhibitory neurons is included, representing the GABAergic neurons that provide inhibition in cortical networks. - These neurons also follow an ML model, but with different conductance values reflecting their inhibitory properties. ### Ionic Currents - **Sodium and Potassium Currents:** - The model includes voltage-gated sodium and potassium channels, mimicking those found in biological neurons. These channels are crucial for the initiation and propagation of action potentials. - The parameters \(g_{Na}\), \(g_{K}\), and their respective reversal potentials (\(E_{Na}\), \(E_K\)) are included, affecting how these ions flow across the membrane. - **Leak Currents:** - Both neuron types have a leak conductance, which allows a constant flow of ions, contributing to the resting membrane potential. ### Synaptic and External Inputs - **Reversal Potentials (\(E_e\), \(E_i\)):** - These variables represent the synaptic reversal potentials for excitatory and inhibitory synapses, modeling the effect of neurotransmitter release on postsynaptic potential changes. - **Synaptic Time Constants:** - These represent the kinetics of synaptic currents, which determine how quickly synaptic effects rise and decay, similar to biological synapses. - **External Input Model:** - External inputs modeled as Poisson processes simulate random synaptic input typical of background neural activity in the cortex. - This setup allows the network to mimic cortical neural responses to external stimuli, modeling how cortical neurons respond to varying input rates. ### Population Dynamics - **Connections and Sparseness:** - Recurrent connections among excitatory and inhibitory populations model realistic sparsity seen in cortical networks (via the sparseness variable \(p\)). - These connections allow for the generation of realistic patterns of network activity, such as oscillations or reverberatory activity commonly observed in brain networks. ### Simulation and Monitoring - **Monitoring Tools:** - State monitors track membrane potentials and gating variables over time, allowing for analysis of network dynamics. - Population rate monitors help in evaluating the overall firing rates, offering insights into excitatory/inhibitory balance and responses to external input. ### Biological Phenomena - **Hysteresis and Nonlinear Dynamics:** - The network includes mechanisms to observe hysteresis phenomena in neural populations, where past inputs can influence the current output due to nonlinear interactions within the network. This is reflective of complex dynamic behaviors observed in cortical networks. Overall, this code models core biophysical properties of neurons and synapses to simulate the dynamics of cortical networks, capturing essential elements of excitatory-inhibitory balance, synaptic integration, and neuronal response to inputs, which are critical for understanding cortical information processing.